## Proof Mooted For Heisenberg's Uncertainty Principle 158 158

ananyo writes

*"Encapsulating the strangeness of quantum mechanics is a single mathematical expression. According to every undergraduate physics textbook, the uncertainty principle states that it is impossible to simultaneously know the exact position and momentum of a subatomic particle — the more precisely one knows the particle's position at a given moment, the less precisely one can know the value of its momentum. But the original version of the principle, put forward by physicist Werner Heisenberg in 1927, couches quantum indeterminism in a different way — as a fundamental limit to how well a detector can measure quantum properties. Heisenberg offered no direct proof for this version of his principle. Now researchers say they have such a proof. (Pre-print available at the arXiv.) If they're right, it would put the measurement aspect of the uncertainty principle on solid ground — something that researchers had started to question — but it would also suggest that quantum-encrypted messages can be transmitted securely."*
## Uncertaintiy principle and Foruier Transforms (Score:5, Interesting)

## I just read the article ( arXiv PDF ) (Score:4, Interesting)

## Proof is already from 1929 (Score:5, Interesting)

Robertson proved in 1929 already the general form of the uncertainty relation. It has nothing to do with Fourier transforms, wavefunctions and disturbance by measurements, but only with the operator character of (some) quantum mechanical observables. I got the proof from this textbook by Stephen Gasiorowicz, unfortunately they skipped this important result from the latest edition (that circulates on internet in the usual places). More information can be found in https://en.wikipedia.org/wiki/Uncertainty_principle#Robertson.E2.80.93Schr.C3.B6dinger_uncertainty_relations [wikipedia.org]

From Quantum Physics by Stephen Gasiorowicz, ISBN 0 471 29281-8

It is important to note that the uncertainty relation

(Delta A)^2 (Delta B)^2 >= \langle i[A,B] \rangle^2 / 2

was derived without any use of the wave concepts or the reciprocity between

a wave form and its fourier transform. The results depends entirely on the

operator properties of the observables A and B.